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- W2419057531 abstract "Lines and Hyperplanes in ℝn are defined. Convex sets are defined and their elementary properties are studied. Separation of sets by hyperplanes is defined and conditions under which various types of separation occur are given. Separation theorems are used to derive alternative theorems for systems of linear inequalities, the most relevant for optimization being Farkas's Lemma. The concepts of supporting hyperplane to a convex set and extreme point of a convex set are introduced and conditions under which they exist are given. Affine geometry is introduced and is used to obtain sharper results concerning separation, support an existence of extreme points." @default.
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- W2419057531 date "2002-01-11" @default.
- W2419057531 modified "2023-09-23" @default.
- W2419057531 title "Convex Sets in ℝn" @default.
- W2419057531 doi "https://doi.org/10.1002/047124970x.ch2" @default.
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